The signatures can be verified with: gpg --verify <file.asc>
You should check that the key fingerprint matches.

Changes from version 3.1.2 to version 3.1.3:
- Better support for Automake 1.13+ (now used to generate the tarball).
- Improved MPFR manual.
- Bug fixes (see <http://www.mpfr.org/mpfr-3.1.2/#fixed> and ChangeLog file).